An Architecture is proposed for Parkinson’s disease detection by investigating the topological properties of functional brain networks within fMRI and EEG Signals of Healthy Control (normal) and PD patients. Figure 1 shows the overview of Proposed Architecture. For fMRI the functional whole-brain connectome was constructed by thresholding partial correlation matrices of 160 regions from Dosenbach brain atlas. 160 x 160 functional correlation matrix was constructed using the Pearson correlation. From the graph theory approach, network metrics were analysed. For EEG spatial and Bispectrum features are extracted. Finally, Adaboost Classifier is used to classify whether it is normal or PD.
Data Set Used:
The input images were taken from the OpenNEURO which is open science neuro informatics database storing datasets from human brain imaging research studies. The dataset contains raw fMRI scans, raw EEG in Brain Vision format where the subjects include fMRI of 100 patients with Parkinson’s and 100 with Healthy control, EEG signals were recorded in closed eye resting state for 100 patients with Parkinson’s and 100 with Healthy Control. In Parkinson’s 25 Male patients and 75 Female patients and in Healthy Control 10 Female and 90 male patients were taken. Figure 2 and Fig. 3 for the input Healthy Control and PD and Fig. 4 and Fig. 5 are Input image EEG for Healthy Control and PD respectively.
Network Construction and functional Connectome
The two fundamental elements of the network are edges and nodes, where nodes represent the brain regions and edges depict the functional connectivity between two brain regions or nodes. The Region of interest for this category are frontoparietal, cingulo-opercular, sensorimotor, occipital, and cerebellum were selected from Dosenbach atlas[ 21] to draw functional connectome and the output is shown in Fig. 6.
GRETNA tool is used to find out the functional connectivity matrices from brain images [20] and edges for the connectivity has been calculated using Pearson corelation coefficients [19]. The output is shown in Fig. 7 and Fig. 8. Each region is considered as a node to construct the brain network and the output is shown in Fig. 9 and Fig. 10.
FEATURE EXTRACTION: fMRI
We have extracted [24] the parameters betweenness mean, betweenness standard deviation, page rank mean, page rank standard deviation, centrality degree mean, centrality degree standard deviation, clustering coefficient, assortivity, closeness, centrality closeness values from network created from fMRI.
Betweenness
$${c}_{Betweenness}=\frac{{\sum }_{v\in \gamma }[{c}_{bet}\left({v}^{*}\right)-{c}_{bet}\left(v\right)] }{{n}^{3}-{4}^{{n}^{2}}+5n-2}$$
1
Where,\({v}^{*}\) is the node with maximum betweenness and \({c}_{bet}(.)\)is the normalized betweenness.
Page rank
$${C}_{PR}=({I-{aAd}^{-1} )}^{-1} 1={D(D-aA)}^{-1}$$
2
Where, \(D\) is a diagonal matrix,\(I\) is an N x N identity matrix, \(a\) is weight on the edges from vertex v.
Centrality Degree
$${C}_{D}\left(i\right)={K}_{i}=\sum _{i\ne j}{A}_{ij}$$
3
Where, \(A\) is a matrix with vertices i ,j where\(i\ne j\)
Clustering Coefficient
$${C}_{clustering}\left(v\right)=\frac{1}{d\left(v\right).(d\left(v\right)-1)}\sum _{r,s\in N\left(v\right)}{A}_{rs}$$
4
Where, \(d\left(v\right)\)is the degree of vertex v,\(N\left(v\right)\) is set of all nodes that are a distance 1 from a vertex v and \(A\) is the matrix.
Assortativity
$${\rho }^{D}=\frac{\sum _{jk} jk({e}_{jk}-{q}_{j }{q}_{k})}{{\sigma }_{q}^{2}}$$
5
Where,\({e}_{jk}\)refers to the joint excess degree probability for nodes with excess degrees j and k. \({q}_{k}\)is a normalized distribution of a randomly selected node, given by \({q}_{k}=\frac{(k+1){p}_{k}}{\sum _{j{j}_{j}^{p}} }\) and \({\sigma }_{q}\) is the standard deviation of the distribution\({q}_{k}\)
Centrality closeness
$${C}_{closeness}\left(v\right)=\frac{1}{\sum _{u\in v} d(u,v)}$$
6
Where, d (u, v) is the distance to all the other nodes in the network.
Feature Extraction: Eeg
The bispectrum is an advanced signal processing technique based on higher order statistics which considers both the amplitude and the degree of phase coupling of a signal. In contrast to traditional power spectrum, which quantifies the power of a time series over frequency, higher order spectral (HOS) analysis employs the Fourier transform of higher order correlation functions to explore the existence of quadratic (and cubic) non-linear coupling information (Rajamanickam Yuvaraj et al,2016).
The extracted bispectrum features are Bispectrum, Cumulant, Element frequency and Lag vectors. Spatial features include Wavelet Coherence mean, Wavelet Coherence SD, Wavelet Cross Spectrum mean, Wavelet Cross Spectrum SD[22].
Bispectrum
$$B({f}_{1 },{f}_{2})=F\left({f}_{1 }\right)*F\left({f}_{2}\right)*{F}^{*}({f}_{1}+{f}_{2})$$
7
Where, F denotes the Fourier transform of the signal, and F* its conjugate.
Cumulant
$${K}_{nz}=\sum _{i=1-n}^{ }{a}_{i}^{n}{k}_{n,{x}_{n}}$$
8
Where, \({k}_{nz}\) represents the nth order of the obtained variable (z). denotes the nth-order cumulant of the \({i}^{th}\) component random variable.\({k}_{n,{x}_{n}}\)
Lag vector
$$LV=\left|⟨sign\left[\varDelta \varnothing ({t}_{k}\right]⟩\right.\left. \right|$$
9
Where, sign is the signum function that discards phase difference of 0 mod π. The LV ranges between 0 and 1, with 0 indicating no coupling of instantaneous coupling due to volume conduction and 1 indicating true, lagged interaction.
Wavelet Cross spectrum
$${wcs}_{jk}^{n}\left(t,s\right)={w}_{j}^{n}(t,s){w}_{k}^{n}{(t,s)}^{*}$$
10
Where, t is the time and s is frequency (scale), as a result the WCS is complex valued
Wavelet Coherence
$$C\left(t,f\right)=\frac{\left| \right.\sum _{i=-\varDelta }^{\varDelta }{pw}_{xy}(T,f,i)\left. \right|}{\sum _{i}{pw}_{xx}(T,f,i)\sum _{i}{pw}_{yy}(T,f,i)}$$
11
Where T is the time around which the coherence is calculated, i is the current index, and f is the frequency. The summations are carried around a variable segment size ∆, which is inversely proportional to frequency
Classification
Using fMRI and EEG signal, we have performed classification operation, to identify whether the input is healthy control or Parkinson affected. In An AdaBoost classifier[24], we have used Naive Bayes classifier as base estimator. In this work, we have used n_estimators as 45 and learning rate as 1. The misclassified training samples get more weights, and the test error keeps decreasing even after 700 iterations.